Warm up: Radicals, Radical & Rational Equations 2/3

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

What is the square root of 24 in simplified form?

Back

The square root of 24 simplifies to 2√6.

Front

How do you solve a rational equation by cross-multiplying?

Back

To solve a rational equation by cross-multiplying, multiply the numerator of one fraction by the denominator of the other fraction and set the two products equal to each other.

Front

What is the cube root of 8?

Back

The cube root of 8 is 2.

Front

What does it mean for an equation to have no solutions?

Back

An equation has no solutions when there are no values that can satisfy the equation, often resulting in a contradiction.

Front

What is the definition of a rational equation?

Back

A rational equation is an equation that involves at least one fraction whose numerator and/or denominator are polynomials.

Front

How do you express x^2 = 9 in radical form?

Back

x = ±√9.

Front

What is the value of x if 2/x = 6/7?

Back

x = 7/3.

Front

What is the principle of simplifying radicals?

Back

The principle of simplifying radicals involves breaking down the radicand into its prime factors and simplifying the expression by taking out pairs of factors.

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction.